Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412

(i) 525

Here we get ,

The remainder is 14 

22² < 525 < 23²

The number to be added will be = 529 - 525 = 4 

Therefore, 525 + 4 = 529

$\sqrt{529} = 23$

 (ii) 1750 

Here we get,

The remainder is 69

41² < 1750 < 42²

The number to be added = 1764 - 1750 = 14

Therefore, 1750 + 14 = 1764

$\sqrt{1764} = 42$

(iii) 252 

Here we get,

The remainder is 27

15² < 252 < 16²

The number to be added = 256 - 252 = 4

Therefore, 252 + 4 = 256

$\sqrt{256} = 16$

(iv) 1825 

Here we get,

The remainder is 61

42² < 1825< 43²

The number to be added = 1849 - 1825 = 24

Therefore, 1825 + 24 = 1849

$\sqrt{1849} = 43$

(v) 6412

Here we get ,

The remainder is 12

80² < 6421< 81²

The number to be added = 6561 - 6412 = 149

Therefore, 6412 + 149 = 6561

$\sqrt{6561} = 81$